Complex Input
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From: John Monro on 16 Nov 2009 02:05 Jerry Avins wrote: > John Monro wrote: > > ... > >> Thanks for that Jerry. I had never heard of the Scott-T transformer. >> The reference was interesting, particularly the way you could see the >> phase relationship clearly from the circuit diagram alone. No need >> for a phasor diagram here! > > There are many attributes of polyphase power distribution that widen > one's horizon. The meeting of that and DSP lies mostly in line- and > motor-protection "relays". (In power circles, a relay is a sensor gizmo > designed to trip a circuit breaker.) > > I know that many see me as the curmudgeon of comp.dsp who claims that > complex numbers, while useful for computation, don't embody reality. > Whatever complex numbers embody, they make it easy for a neophyte to > imagine unreality. The abstraction they represent allows one to skip > altogether the abstracted concepts. That happens in other areas too. Maybe the issue is that you prefer one abstracton over another, in particular methods that use geometry for analysing signals over methods that use complex maths. Most in this group will have used geometric interpretions of waveform phenomena for so long that it seems obvious but in fact it is not at all obvious that there is any connection between a waveform and an angle. You can't see the angle on a CRO for example. This is an abstraction that beginners have to cope with. The concept of a waveform obvious to us, but is another example of an abstraction. I think that we are in agreement that complex numbers are necessary at some point when roblems in DSP become just too tedious to solve geometrically. We probably differ on the point at which we abandon the geometric methods and go to complex methods. This is an important educational consideration and one on which everyone will have their own view. > In a recent thread, a newbie wondered how to convert PCM to integer. You > must be aware of my being asked by a CS graduate how computer hardware > distinguishes between ASCII and bite-wide integers, and blowing me off > in disbelief when explained. (I repeat it often enough.) I have had a similar experience with this exact question being asked. You may also be > aware of Richard Feynman's disappointment by that the Brazilian graduate > student he was interviewing. The student knew plane-parallel refraction > theoretically, but couldn't think of an instance of it, not even a > window pane. Whatever the mathematics, if you don't know how it works, > you don't know what you're talking _about_, quantum mechanics excepted. Yes, and also the one where Feynman tells his classmates (at MSc level I think)that a French Curve drafting template has its curve generated by a special function with the property that the slope at the top of the template is zero whichever way you hold it. Much amusement as he watches them check out this particular instance of a mathematical fact that they already knew from their undergraduate maths studies. > > An example from polyphase power, which is where we started. Balanced > three-phase systems are fairly easy to deal with. (More on this later.*) > Unbalanced systems, those in which the phase currents differ (and with > faults, also the phase voltages) are more complicated. One way to > regularize the subject is decomposing the into "symmetrical components" > (http://en.wikipedia.org/wiki/Symmetrical_components) which consist of > positive (A B C) and negative sequence (A C B) balanced currents, and > zero sequence currents which have the same magnitude and phase in all > lines. When their coefficients are appropriately chosen, the > superposition of these components represents the actual currents. The > abstraction is so useful that some people always deal with three-phase > circuits this way. > > "It can be shown" that two wattmeters suffice to measure the total power > delivered by a three-phase system. A standard three-meter installation > in a wye-connected system consists of a current coil in each line ans > the corresponding voltage coil from line to neutral; basically, three > single-phase meters. It gets more interesting in a delta-connected > system because there is no neutral. If the voltage coils have the same > impedance, connecting them together and letting the node float to create > a virtual neutral works. What happens if the impedances differ? Analysis > with line phasors is straightforward. With symmetrical components, it is > long and difficult. Yet I have seen it done that way because symmetrical > components are "real" and the actual line phasors are "derived". Bah! So the more abstract method is the one that would be preferred in practice in this case. Not a criticism, just an observation. > > The upshot of the analysis is that, so long as one cares only about the > total power, it doesn't matter what the node voltage is. The node can be > tied to one of the lines, effectively shorting out one of the meters. I > have a simple proof of that case which makes no use of symmetrical > components and little use of line phasors. Connect the current coils and > one side of the corresponding voltage coils to lines A and B, and the > other ends of the voltage coils to line C. Connect a load from A to C. > one meter correctly indicated the power in that line. Likewise for a > load from B to C. Connect a load from A to B. Two current coils sense > it, while the voltage coils see a voltage 60 degrees out of phase. The > power is then 2*I*V(cos(60) = VI. Power is additive: Q.E.D > > It is important in engineering to deal with what is there and not > scratch one's left ear with the right hand behind one's back. I chose > examples peripheral to DSP in the hope that newness will allow a fresh > view. > > Jerry > ________________________________ > * Long ago, in order to get credit for a Fourier analysis course I had > taken in another school, I had to pass an evaluation test. It turned out > to be a regular class exam about 3/4 of the way through the semester. It > consisted of one question: "A balanced three-phase wye-connected system > delivers square waves to a balanced resistive load. Describe the neutral > current." (Three-phase circuits were covered in an prerequisite course.) > The key word was "describe". I first did it graphically. At any instant, > two phases have the same polarity and the other is opposite, so the > magnitude of the neutral current is the same as any of the phases. Every > time any phase undergoes a zero crossing, the neutral polarity reverses, > so the neutral current has three times the frequency of the line > currents. Period. End of story. I admit that this startled me because there is no way that a linear combination of sinusoids at a frequency of F can generate a signal with a frequency of 3F. Then I remembered that we are talking about square waves, and there is already a strong 3F component present. Of course I had never even heard of the 'three-phase theorem,' not knowing a lot about three-phase power. Regards, John Still, engineering is math, so I figured > I better supply an equation as well as a graph. I turned the page in the > exam book and wrote out the series for a square wave, describing one > phase. (You don't derive the quadratic formula every time you need it. > Why should a square wave be different?) I didn't time-shift it to get > the other two phases and go through the trig to combine them. Instead, I > invoked a three-phase theorem (from the prerequisite; it was legit): in > a wye system, harmonics divisible by three add in the neutral, the > others cancel. So I put a 3 in front of the 4/pi, and crossed out the > appropriate terms. Then, to ice the cake -- I already knew the answer, I > took the 3 inside the brackets, canceling one factor of three in all the > denominators and replaced 3f with f'. Voila! a square wave in f'. Total > elapsed time, about 6 minutes. One other fellow got the right answer. He > was a math whiz. He derived the square wave, time shifted it, added, > canceling some terms and tripling the rest but omitted the neat f' > substitution, and so didn't visualize the actual wave shape. A few > others nearly made it but ran out of time (50 minutes.) > > When I turned in the exam book, the prof sympathetically told me to try, > that I didn't have to be perfect. I whispered that I thought I had > completed it. He looked, wrinkling his nose at the graph. It was clearly > correct, but not really what he wanted. I whispered again, "There's > more. Turn the page." He did, and in a second, gave me a thumbs up.
From: Rune Allnor on 16 Nov 2009 05:45 On 14 Nov, 14:50, Jerry Avins <j...(a)ieee.org> wrote: >, Which leg of a two-phase 220VAC power line gives > imaginary shocks? I was once very close to setting an electromotor on fire, using imaginary power [*]. We used a 60Hz motor from a 50Hz power supply. The thing would have caught fire, were it not for the internal heat fuses etc in the motor. Rune [*] Reactive power, that is caused by internal currents to the device. The energy in these currents only produce heat, and can not be converted to external work. These phenomena are easily described by complex-valued maths, where they could appear as an imaginary component of power. It is interesting to note that the textbook on electrical power systems we used ages ago cautiously and carefully avoid using imaginary arithmetics when talking about reactive power...
From: Vladimir Vassilevsky on 16 Nov 2009 12:08 Rune Allnor wrote: > I was once very close to setting an electromotor on fire, > using imaginary power [*]. We used a 60Hz motor from a 50Hz > power supply. Using 60Hz motor at 50Hz requires power of imagination. This is what was probably meant by F. Bacon in his famous "knowledge is power". VLV
From: Rune Allnor on 16 Nov 2009 12:33 On 16 Nov, 18:08, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote: > Rune Allnor wrote: > > I was once very close to setting an electromotor on fire, > > using imaginary power [*]. We used a 60Hz motor from a 50Hz > > power supply. > > Using 60Hz motor at 50Hz requires power of imagination. > This is what was probably meant by F. Bacon in his famous "knowledge is > power". Don't know Bacon, but somebody were close to frying when I discovered why the problem occured in the first place: We had a transformer onboard, that was labeled something like "50-60 Hz" (meaning that it could be used in either 50Hz or 60Hz systems), but whoever was responsible for the instrumentation had beliebved it to mean "converts from 50Hz to 60Hz". Suffice it to say that people walked *very* quietly around me for days afterwards. Rune
From: Vladimir Vassilevsky on 16 Nov 2009 12:54
Rune Allnor wrote: > On 16 Nov, 18:08, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote: > >>Rune Allnor wrote: >> >>>I was once very close to setting an electromotor on fire, >>>using imaginary power [*]. We used a 60Hz motor from a 50Hz >>>power supply. >> >>Using 60Hz motor at 50Hz requires power of imagination. >>This is what was probably meant by F. Bacon in his famous "knowledge is >>power". > > > Don't know Bacon, but somebody were close to frying when > I discovered why the problem occured in the first place: > We had a transformer onboard, that was labeled something > like "50-60 Hz" (meaning that it could be used in either > 50Hz or 60Hz systems), but whoever was responsible for > the instrumentation had beliebved it to mean "converts > from 50Hz to 60Hz". > Suffice it to say that people walked *very* quietly around > me for days afterwards. When we moved to US, I tried to find a multisystem VCR so it would be compatible with old tapes recorded in PAL. Surprisingly nobody ever heard about a difference in the TV standards, but they immediately suggested 120/220V transformers. BTW, Rune, if you don't mind, would you please write few words about yourself and send to me. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com |